(a) Work through the derivation of Eq. (7.73) for the scaled time delay in the vicinity of the cusp caustic for our simple example [Eq. (7.68)], with the aid of a suitable change of variables.

(b) Sketch the nesting of the contours for the elliptic umbilic catastrophe as shown for the other four catastrophes in Fig. 7.14. Verify that Eq. (7.81) describes this catastrophe.

Equations.

Figure 7.14

Transcribed Image Text:

t = tgeo + tlens = a² 2fzc f-z+ a²z 25² (7.68)